In a typical scientific computing centre, several applications coexist and share a single physical infrastructure. An underlying Private Cloud infrastructure eases the management and maintenance of such heterogeneous applications (such as multipurpose or application-specific batch farms, Grid sites, interactive data analysis facilities and others), allowing dynamic allocation resources to any application. Furthermore, the maintenance of large deployments of complex and rapidly evolving middleware and application software is eased by the use of virtual images and contextualization techniques. Such infrastructures are being deployed in some large centres (see e.g. the CERN Agile Infrastructure project), but with several open-source tools reaching maturity this is becoming viable also for smaller sites. In this contribution we describe the Private Cloud infrastructure at the INFN-Torino Computer Centre, that hosts a full-fledged WLCG Tier-2 centre, an Interactive Analysis Facility for the ALICE experiment at the CERN LHC and several smaller scientific computing applications. The private cloud building blocks include the OpenNebula software stack, the GlusterFS filesystem and the OpenWRT Linux distribution (used for network virtualization); a future integration into a federated higher-level infrastructure is made possible by exposing commonly used APIs like EC2 and OCCI.